Mathematics

Mathematics at St. Michael’s

At St. Michael’s, mathematics is brought to life through hands-on, purposeful learning that equips children with the knowledge, strategies, and confidence to become fluent and flexible problem solvers. We believe that all pupils should be empowered to understand, enjoy, and apply mathematics meaningfully—both in the classroom and in the wider world.

Our Approach

We follow the White Rose Maths Scheme of Learning from Early Years through to Year 6. Our curriculum is carefully sequenced and structured to build secure understanding in:

  • Fluency: developing rapid recall of key facts and methods
  • Reasoning: explaining and justifying mathematical thinking
  • Problem Solving: applying learning to a range of contexts

Daily teaching is underpinned by the CPA approach—concrete, pictorial and abstract representations—which allows pupils to build deep and lasting conceptual understanding. Each lesson begins with focused revision and key skill development to reinforce core knowledge and accelerate progress.

Mathematical Foundations: Core Elements

  • Daily Key Skills: Regular practice in arithmetic, number facts, and operations to strengthen fluency.
  • Times Tables: Engaging practice through TT Rockstars, Numbots, and CGP Daily Practice Books to improve speed and accuracy.
  • White Rose ‘Small Steps’: Incremental, progressive learning aligned to the Ready to Progress criteria.
  • Revision & Reinforcement: Morning fluency sessions using retrieval strategies and guided revision.
  • Targeted Interventions: Programmes such as Mastering Number and individualised fluency support ensure every child is supported.

Understanding Through Knowledge Types

We structure our curriculum to develop three key forms of mathematical knowledge:

1. Declarative Knowledge

“I know that…”
Children learn core facts and concepts, such as number bonds, properties of shape, and key mathematical vocabulary. These are explicitly taught and regularly revisited to form a secure foundation.

2. Procedural Knowledge

“I know how…”
We teach clear, consistent methods for carrying out mathematical operations using a CPA approach:

  • Concrete – physically handling resources (e.g. counters, base 10)
  • Pictorial – using visual models and diagrams
  • Abstract – representing concepts using symbols and written notation

Pupils move flexibly between each stage, building mental connections and confidence in tackling problems independently.

3. Conditional Knowledge

“I know when and why…”
Children learn to choose and apply the most effective strategies based on the problem presented. This critical step combines facts and methods into flexible, transferable thinking—empowering pupils to reason, explain, and solve both routine and unfamiliar problems.

Our Intent for Every Learner

We aim for every child at St. Michael’s to:

  • Build fluency in the fundamentals of maths
  • Develop a deep and adaptable understanding of concepts
  • Apply knowledge confidently to reasoning and problem solving tasks
  • Use mathematical language to explain and justify their thinking
  • Transfer key skills across the wider curriculum and into the real world

Mathematics at St. Michael’s is not just about getting the answer—it’s about understanding how and why. Through carefully crafted teaching and rich opportunities for exploration, we nurture children who are curious, confident, and capable mathematicians.

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Mathematics Implementation at St. Michael’s

Our mathematics curriculum is rooted in the National Curriculum and delivered through the White Rose Maths Scheme of Learning, which provides a clear and progressive framework from Early Years through to Year 6. This structured approach ensures that children develop a deep, connected understanding of mathematical concepts over time.

Using White Rose materials—including the Small Steps progression and Ready to Progress criteria—lessons are broken down into manageable, well-sequenced steps that focus on building secure knowledge in three key domains:

  • Declarative Knowledge (I know that…) – core facts and vocabulary
  • Procedural Knowledge (I know how…) – methods and techniques
  • Conditional Knowledge (I know when and why…) – strategies for reasoning and problem solving

These types of knowledge are explicitly explored with pupils, helping them understand how mathematics works and how to apply it flexibly.

Curriculum Delivery: Key Features

To bring our mathematics vision to life, we implement the curriculum through:

  • White Rose Maths schemes across EYFS, KS1, and KS2
  • NCETM Mastering Number Programme in EYFS and KS1, developing number sense, fluency, and flexibility
  • Daily Maths Lessons focused on acquiring, revisiting, and building knowledge of facts, methods, and strategies
  • High-Quality Teaching tailored to meet the needs of all learners
  • CPA Approach (Concrete–Pictorial–Abstract), supporting conceptual understanding through a variety of manipulatives and representations
  • Learning Environments rich in mathematical vocabulary and challenge, including working walls and hands-on resources
  • Progressive Times Tables Strategy supported by TT Rockstars, Numbots, and additional fluency tools
  • Targeted Support through high-impact intervention and booster programmes

At St. Michael’s, we are committed to ensuring that every child builds a strong mathematical foundation—equipping them with the confidence, fluency, and problem-solving skills they need to thrive in school and beyond.

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Memory and Mastery: Securing Mathematical Understanding

At St. Michael’s, we believe that meaningful learning in mathematics is built on strong foundations. Our curriculum is carefully sequenced to ensure that children develop fluency with simpler concepts before progressing to more complex ones. For example, pupils learn to understand the value of numbers before applying that knowledge to addition and subtraction.

Each unit of learning is organised into conceptual blocks, and within each block, learning progresses through small, purposeful steps. Take our Year 3 Addition and Subtraction block: it begins with adding and subtracting multiples of 100 and gradually builds in complexity—step by step, concept by concept. Each new step builds directly on prior knowledge, ensuring no gaps and no guesswork.

Making Learning Stick

Our curriculum actively supports retention and transfer of knowledge. Skills introduced in one context are later revisited and applied in others—a strategy known as interleaving. In Year 3, for example, the addition and subtraction strategies pupils learn early on are woven into later blocks such as:

  • Multiplication and Division
  • Money
  • Length and Perimeter
  • Mass and Capacity

This revisiting reinforces understanding and strengthens long-term memory.

To support this further, we make use of the White Rose Maths premium resources, including:

  • Flashback 4: a daily review prompt drawing on learning from yesterday, last week, last month, and last term
  • True or False: powerful prompts for revisiting core concepts and provoking discussion

Combining Mastery with Spiral Learning

Our curriculum design draws on the best of both mastery and spiral approaches:

  • Like a mastery approach, we spend longer on key topics, aiming for depth, cohesion and confidence
  • Like a spiral curriculum, we know that understanding deepens over time and through repeated exposure in new contexts

We hold a fundamental belief: that with effort, clarity, and the right support, all pupils are capable of succeeding in mathematics.

Fluency, Reasoning and Problem Solving – Every Step of the Way

In every lesson, these three pillars of mathematical success are woven together—not taught in isolation. We don’t complete all the fluency first, followed by reasoning, and then problem solving. Instead, these elements are interwoven, often introduced through purposeful problems that require fluency to resolve.

For instance, children may first encounter division within a real-world sharing context, supporting both conceptual understanding and procedural accuracy from the outset.

Early Mathematical Foundations in EYFS

At St. Michael’s, our mathematics curriculum in the Early Years Foundation Stage (EYFS) reflects the ethos of early childhood education—playful, purposeful, and deeply rooted in exploration. We provide a mathematically rich environment that nurtures curiosity, builds confidence, and lays the foundations for lifelong learning.

We follow the White Rose Maths EYFS scheme, which is thoughtfully structured into ten progressive phases. These offer children engaging, hands-on opportunities to explore number, shape, measure, and spatial thinking. The sequence is designed to revisit and deepen understanding throughout the year, enabling children to connect concepts and apply them with increasing independence.

To strengthen number sense and fluency, our Reception team also implements the Mastering Number Programme, delivered alongside the White Rose curriculum. This nationally recognised programme focuses on securing the core knowledge and understanding essential for Reception and beyond.

Together, these approaches ensure our youngest learners develop a strong conceptual understanding and a love of mathematics from the very start of their journey.

Mathematics Pedagogy 

Whole-Class Teaching with Tailored Support

At St. Michael’s, our approach to mathematics is grounded in the belief that all pupils can achieve with the right support and depth of understanding. We teach the whole class together, progressing through topics at broadly the same pace. This ensures every child begins with equal access to high-quality mathematical instruction, with flexible support and challenge built in as needed.

Each topic is explored in depth, and we do not move on until pupils demonstrate secure understanding. This slower, more deliberate pace fosters deep relational understanding, allowing children to build meaningful connections rather than relying on rote procedures.

Depth Before Acceleration

All pupils are given time to think deeply, reason logically, and consolidate their learning. For those who grasp concepts quickly, we provide enrichment through sophisticated problem-solving tasks, encouraging them to apply their knowledge in complex, unfamiliar contexts. For pupils who need more time, in-lesson scaffolding and same-day intervention ensure that no child is left behind. This adaptive support may happen during the lesson or through targeted follow-up later that day.

Concrete–Pictorial–Abstract: A Journey to Understanding

Central to our teaching is the Concrete–Pictorial–Abstract (CPA) approach, a well-researched and highly effective framework for learning. Developed by Jerome Bruner, this method allows children to:

  • Concrete: Begin with hands-on, physical resources to model concepts
  • Pictorial: Move to visual representations and diagrams
  • Abstract: Progress to symbolic and formal notation once understanding is secure

Teachers move fluidly between these stages, ensuring that pupils develop a deep, sustainable understanding of mathematical ideas. The CPA model is a cornerstone of the Singapore Maths mastery approach and is used consistently across our school to support all learners.

Understanding the CPA Approach: Concrete – Pictorial – Abstract

At St. Michael’s, we use the CPA approach as a core part of our maths mastery strategy. Based on the research of psychologist Jerome Bruner, CPA is a powerful teaching framework that moves pupils from hands-on experience to deep conceptual understanding. It’s especially effective in developing fluency with more abstract concepts such as fractions.

Together with bar modelling and number bonds, CPA is essential to our teaching of number and calculation.

Concrete: Learning by Doing

This is the stage where learning is tangible. Children use real, physical objects—counters, cubes, number rods, and other manipulatives—to model and explore problems. Rather than watching a demonstration, pupils interact directly with mathematical ideas, making learning meaningful and memorable.

Pictorial: Learning by Seeing

Next, pupils move to visual representations. Diagrams, number lines, bar models, and drawings help children bridge their understanding from concrete resources to abstract concepts. These images help internalise the maths and support learners in making sense of more challenging ideas—like regrouping or comparing fractions.

Abstract: Learning by Thinking

Once understanding is secure, children work with symbolic representations: numerals, symbols, and formal written methods. This stage involves using standard mathematical notation (e.g. +, –, ×, ÷) to represent and solve problems. Pupils reach this phase only when they have strong foundations from the concrete and pictorial stages.

By using the CPA model consistently across year groups, we support pupils in developing a deep, sustainable understanding of mathematics, not just procedural fluency. It’s a framework that allows all learners to build confidence, make connections, and achieve mastery.

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